Handicappers for greyhound races express their belief about the probabilities that each greyhound will win a race in terms of odds. If the probability of event E is P(E), then the odds in favor of E are P(E) to 1 - P(E). Thus, if a handicapper assesses a probability of .25 that Oxford Shoes will win its next race, the odds in favor of Oxford Shoes are 25/100 to 75/100, or 1 to 3. It follows that the odds against E are 1 - P(E) to P(E), or 3 to 1 against a win by Oxford Shoes. In general, if the odds in favor of event E are a to b, then P(E) = a/(a + b).
a. A second handicapper assesses the probability of a win by Oxford Shoes to be 1/3. According to the second handicapper, what are the odds in favor of Oxford Shoes winning?
b. A third handicapper assesses the odds in favor of Oxford Shoes to be 1 to 1. According to the third handicapper, what is the probability of Oxford Shoes winning?
c. A fourth handicapper assesses the odds against Oxford Shoes winning to be 3 to 2. Find this handicapper's assessment of the probability that Oxford Shoes will win.